The 803Di is overall the better loudspeaker as you would hope (and expect) for a newer version. But it is not a dramatic improvement - move akin to a BMW mid-life automobile face-lift where the engine has been upgraded and and a few cosmetic exterior changes applied. The only cosmetic update I really appreciate is the magnetically attached grille - makes it easy to remove for serious listening.
The 803Di is marginally more detailed in midrange and treble, and has a tighter and more articulate bass. The 803D midrange and treble are better matched in sensitivity whereas the 803 Diamond treble balance sounds slightly tilted up.
Overall I think the 803D is better balanced tonally for relaxed listening whereas the 803Diamond is a touch more upfront and rewards more focused listening sessions.
The 803Di is marginally more detailed in midrange and treble, and has a tighter and more articulate bass. The 803D midrange and treble are better matched in sensitivity whereas the 803 Diamond treble balance sounds slightly tilted up.
Overall I think the 803D is better balanced tonally for relaxed listening whereas the 803Diamond is a touch more upfront and rewards more focused listening sessions.